Bispectral Analysis Of Randomly Sampled Data

. A continuous time series is often observed or sampled at discrete intervals. Most literature has dealt with the case when the sampling intervals are equally spaced. For irregularly sampled data, most existing literature is concerned with second‐order moments or anti‐aliasing spectral estimations. We study the estimation of higher‐order spectral density functions with the emphasis on the bispectral estimate when the continuous time series is sampled by a random point process. Estimates under the Poisson sampling scheme are studied in detail. Asymptotic bias and covariances are obtained. In particular, it is shown explicitly how the information of the sampling process comes into play in obtaining a consistent estimate of the bispectral density function of a continuous time series. In contrast to the second‐order spectral density function estimation where the Poisson sampling scheme results in a constant correction term, a consistent bispectral density function estimate results in a nonlinear correction term even in the Poisson sampling scheme. A simple simulation example is presented for illustration.